Alterations in hemodynamics have been linked to wide-ranging cardiac and vascular conditions, including cardiomyopathy, atrial fibrillation, valvular abnormalities, aortic atherosclerosis and aneurysm, congenital heart disease, renal stenosis, portal hypertension due to liver cirrhosis, intracranial aneurysm and stenosis, and peripheral arterial disease. Among the clinical tools available to investigate blood velocity, Doppler ultrasound is a popular choice. However, in many patients (e.g., those suffering from obesity or chronic lung disease) the results are sub-optimal due to poor acoustic windows or misalignment between the ultrasound beam and the blood flow. Also, in the case of valvular stenosis, heavy calcification of the aortic valve or significant flow acceleration in the left ventricular outflow tract may obscure assessment of the aortic valve.
Phase-contrast MRI (PC-MRI) is not limited by the acoustic windows of ultrasound, and can be used in combination with other MRI techniques for a comprehensive evaluation of patients with known or suspected cardiovascular disease. PC-MRI enables quantification of several hemodynamic parameters, including flow volume and peak velocity, and is used routinely to assess patients with congenital heart disease and valvular abnormalities. When extended to three spatial dimensions and three directions of velocity (4D flow), more sophisticated parameters such as wall shear stress, pulse wave velocity, turbulence intensity, and 3D pressure gradients can also be extracted to provide a comprehensive characterization of the cardiovascular system that is not available otherwise.
Flow information in PC-MRI is encoded into the phase of the complex-valued image. This information is then retrieved by measuring the pixel-wise phase difference between images collected under different values of the velocity-encoding (VENC) gradients. Inadvertently, PC-MRI measurements also encode phase due to gradient waveform distortions, which cannot be removed by pixel-wise phase subtraction, resulting in a residual background phase (BP). Studies have shown that BP can introduce significant errors in the quantification of flow volume, which involves spatial and temporal integration of the blood velocity and thus accumulates BP errors over space and time. BP due to concomitant gradients can be corrected with reasonable accuracy; however, accounting for eddy currents-induced BP (EC-BP) has not been satisfactorily addressed. As the clinical utility of cardiac MRI expands, it is important that clinicians trust the flow volume measurements, which cannot be achieved without addressing the issue of EC-BP.
One method that has been proposed to correct for EC-BP is to perform a separate experiment using a static phantom. In this method, the phantom measurements are performed after removing the patient from the scanner and by repeating the same pulse sequence that was used for in vivo measurements. The BP obtained from the static phantom is subtracted directly from the in vivo phase map. For multi-directional encoding, the process of subtraction is repeated for all encoding directions. This method, despite being robust, is not an attractive option because of the significant extra time required to perform phantom imaging for each clinical sequence performed. Another widely reported method to correct BP relies on fitting and subtracting a polynomial surface to the pixels within regions of static tissue. To employ higher order polynomials, which have been shown to improve the accuracy of BP correction, this method requires sufficient static tissue in close proximity to the region of interest—a requirement that cannot be met for imaging of the heart or great vessels in the thorax that are generally surrounded by air (which is devoid of MRI signal) in the lungs.
The challenges associated with this method are depicted in FIG. 1, which illustrates a time-averaged phase map 102 after applying correction for concomitant gradients, BP correction maps obtained by least squares fitting with 1st and 5th order polynomials (104 and 108, respectively), and the corrected phase maps after applying the 1st order and 5th order corrections (106 and 110, respectively). As shown in FIG. 1, the display range is ±5% of the VENC. In FIG. 1, the results are shown for a routine PC-MRI acquisition performed on a juvenile subject using a clinical scanner (1.5T MAGNETOM Aera, Siemens Healthcare, Erlangen, Germany). As shown in FIG. 1, least squares fitting on pixels within static tissue gives widely different results when polynomials of 1st and 5th orders are used. A pixel was regarded as static if its temporal standard deviation was in the bottom quartile. The phase difference between the two corrections around the heart region is 0.8% of the VENC, which implies that flow volume quantification cannot be simultaneously accurate for both corrections.
On one hand, the 1st order polynomial fitting exhibits signs of under-fitting as evidenced by the residual background phase in the corrected map (104). On the other hand, the 5th order polynomial fitting may very well result in an over-fitting, especially in regions away from the static tissue. The example of FIG. 1 highlights the instability associated with polynomial fitting when the static tissue is distal to the area of interest. This example also highlights the problem of selecting an appropriate polynomial order. Higher order polynomials have been shown to improve accuracy, but in the absence of adequate data (pixels from static tissue) higher order polynomial fitting can generate erroneous results. Similar results were observed when weighted least squares was employed instead of explicit classification of pixels into static and non-static regions. Thus, current methods fall short of fully addressing the BP correction issue that affects every PC-MRI acquisition.